I think my situation was a little more drastic than yours at this moment. I don't mean to downplay yours tho. The lack of remorse and blame shifting is incredibly painful by itself. Trust me, I know.
While my wife ended the physical relationship, ceased most communications outside of work, and claimed it was a "just friends" situation now, it still felt insincere and she wasn't very remorseful.
I broke down and got into her messages. Her thread with him was set up for auto delete so I couldn't see what was said, but I saw the frequency and more than a few voice chats, some as long as 3½ hours.
She had all of her messages with her friends intact tho, and I read those and discovered that she had lied to me about the depth of their relationship, was still pining for him, and was saying unflattering things about me. What I read that day gutted me. It made my decision much easier. I had decided that if I had to live with someone who was remorseless and lacked basic decency and respect my life was just going to be miserable.
When she got home from work I confronted her about her messages and she tried to downplay them, even knowing I had just read them. I said something very similar to what The1stWife said and told her if she wanted him she could have him and started calling lawyers. She stood there and watched me set up 3 consultations. I was very calm, cool, and resigned, but on the inside I was screaming "FOR CHRIST'S SAKE, STOP ME FROM DOING THIS!"
When I started talking about how we were going to handle the house and looking up real estate agents she broke in a way I'd never seen her break before. She was hysterical. I don't think she thought I'd really do it, but I had reached my limit.
I don't know if you've had that moment yet, but even when I thought we were done and I was making those calls there was a sense of relief and liberation. I was getting out of a horrible situation one way or another. If that meant divorce, then so be it.
From what you're typing it doesn't sound like your husband is remorseful and I think your instinct might be right. He might be waiting for you to pull the trigger so he doesn't have to. If that's the case I'm so sorry that you're in this position, but you have to ask yourself if you're willing to continue living with a coward who doesn't want to be there anyway.
You're not the bad guy here. Even if you initiate a divorce and he tells you its your fault for ending the marriage he's the one who ended it by cheating on you. That's what killed it. Not you for not wanting to be with a remorseless unrepentant cheater.
The old marriage is permanently dead. The only hope is to build a new one on a new foundation built on transparency, trust, and respect. And it will take both if you to do the work of laying that foundation. Otherwise it's just going to be a continuation of the marriage that led to this disaster to begin with. You have to decide what you want, and then stick to your guns, accept your decision, and follow through with it.
BB gave you some great advice above. Starting the divorce process isn't the same as instantly ending the marriage. It takes time and you can pause or stop it altogether if there's a miracle turnaround and he comes to his senses. I think you should at the very least get a few free consultations, if possible, and at least get an idea of what you'd be facing if it comes to it. You don't even necessarily have to tell him you're doing it if you're not ready, and it will take some of the fear of the unknown out of the equation for you.
Sending virtual hugs your way.